Yeah, I think that you don't understand me. You suggest: 1 - pnorm(Threshold,mean,sd) = Probability that rnorm(1,mean,sd) > Threshold
I want to know: Probability that quantile(rnorm(n,mean,sd),prob) > Threshold I use rnorm() to simulate a sample of size n and then I compute the statistic from that sample using quantile(). Like all statistics, that quantile stat (which is a weighted average of 2 order statistics) is a function of the realized data and hence has a sampling distribution. I want to compute the cdf of that sampling distribution. Even own the David and Nagaraja _Order Statistics_ text in my library does not have a closed-form cdf for that statistic... On Mon, Feb 14, 2011 at 2:20 PM, Jonathan P Daily <jda...@usgs.gov> wrote: > If I understand this, you have a value x, or a vector of values x, and you > want to know the CDF that this value is drawn from a normal distribution? > > I assume you are drawing from rnorm for your simulations, so look at the > other functions listed when you ?rnorm. > > HTH > -------------------------------------- > Jonathan P. Daily > Technician - USGS Leetown Science Center > 11649 Leetown Road > Kearneysville WV, 25430 > (304) 724-4480 > "Is the room still a room when its empty? Does the room, > the thing itself have purpose? Or do we, what's the word... imbue it." > - Jubal Early, Firefly > > r-help-boun...@r-project.org wrote on 02/14/2011 09:58:09 AM: > > > [image removed] > > > > [R] CDF of Sample Quantile > > > > Bentley Coffey > > > > to: > > > > r-help > > > > 02/14/2011 01:58 PM > > > > Sent by: > > > > r-help-boun...@r-project.org > > > > I need to calculate the probability that a sample quantile will exceed a > > threshold given the size of the iid sample and the parameters describing > the > > distribution of each observation (normal, in my case). I can compute the > > probability with brute force simulation: simulate a size N sample, apply > R's > > quantile() function on it, compare it to the threshold, replicate this > MANY > > times, and count the number of times the sample quantile exceeded the > > threshold (dividing by the total number of replications yields the > > probability of interest). The problem is that the number of replications > > required to get sufficient precision (3 digits say) is so HUGE that this > > takes FOREVER. I have to perform this task so much in my script > (searching > > over the sample size and repeated for several different distribution > > parameters) that it takes too many hours to run. > > > > I've searched for pre-existing code to do this in R and haven't found > > anything. Perhaps I'm missing something. Is anyone aware of an R > function to > > compute this probability? > > > > I've tried writing my own code using the fact that R's quantile() > function > > is a linear combination of 2 order statistics. Basically, I wrote down > the > > mathematical form of the joint pdf for the 2 order statistics (a > function of > > the sample size and the distribution parameters) then performed a > > pseudo-Monte Carlo integration (i.e. using Halton Draws rather than R's > > random draws) over the region where the sample quantile exceeds the > > threshold. In theory, this should work and it takes about 1000 times > fewer > > clock cycles to compute than the Brute Force approach. My problem is > that > > there is a significant discrepancy between the results using Brute Force > and > > using this more efficient approach that I have coded up. I believe that > the > > problem is numerical error but it could be some programming bug; > regardless, > > I have been unable to locate the source of this problem and have spent > over > > 20 hours trying to identify it this weekend. Please, somebody help!!! > > > > So, again, my question: is there code in R for quickly evaluating the > CDF of > > a Sample Quantile given the sample size and the parameters governing the > > distribution of each iid point in the sample? > > > > Grateful for any help, > > > > Bentley > > > > [[alternative HTML version deleted]] > > > > ______________________________________________ > > R-help@r-project.org mailing list > > https://stat.ethz.ch/mailman/listinfo/r-help > > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > > and provide commented, minimal, self-contained, reproducible code. > > [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
